To determine the net profit for the retailer based on the information provided, we will break down the problem step-by-step.
Step 1: Understand the Selling Price Calculation
The retailer adds one-quarter (25%) to the cost of the article to determine the selling price. This means if the cost of an article is ( C ), the selling price ( SP ) can be calculated as follows:
[
SP = C + \frac{1}{4}C = C \times \left(1 + \frac{1}{4}\right) = C \times \frac{5}{4}
]
Step 2: Calculate the Cost of Goods Sold (COGS)
Given that the total sales amount to N23,000, we can find the cost of goods sold (COGS) using the relationship between sales and cost. Since the selling price is 125% of the cost, we can express the total sales in terms of COGS.
Let ( COGS ) be the total cost of goods sold. The relationship can be expressed as:
[
Total\ Sales = Selling\ Price \times Quantity
]
Since the selling price is ( \frac{5}{4} ) of the cost, we can express the total sales as:
[
Total\ Sales = \frac{5}{4} \times COGS
]
Setting this equal to the total sales of N23,000:
[
N23,000 = \frac{5}{4} \times COGS
]
To find COGS, we rearrange the equation:
[
COGS = N23,000 \times \frac{4}{5} = N18,400
]
Step 3: Calculate the Retailer's Expenses
The retailer's expenses are given as 10% of his sales. Therefore, we can calculate the expenses as follows:
[
Expenses = 10\% \times Total\ Sales = 0.10 \times N23,000 = N2,300
]
Step 4: Calculate the Net Profit
Net profit can be calculated using the formula:
[
Net\ Profit = Total\ Sales - COGS - Expenses
]
Substituting the values we have calculated:
[
Net\ Profit = N23,000 - N18,400 - N2,300
]
Calculating this step-by-step:
- Calculate ( N23,000 - N18,400 = N4,600 )
- Then, subtract the expenses: ( N4,600 - N2,300 = N2,300 )
Thus, the net profit for the year is
N2,300.
Conclusion: Correct Option
The correct option is
D. N2,300.
Explanation of Other Options
- A. N5,750: This option is incorrect because it does not account for the correct calculation of COGS and expenses.
- B. N5,650: This option is also incorrect for the same reasons as option A; it miscalculates the expenses and COGS.
- C. N3,200: This option is incorrect as it miscalculates the net profit by not properly accounting for the expenses and COGS.
Revision Summary
- The selling price is calculated by adding 25% to the cost of goods sold.
- Total sales of N23,000 lead to a COGS of N18,400.
- Retailer expenses are 10% of sales, amounting to N2,300.
- The net profit is calculated as Total Sales minus COGS and Expenses, resulting in N2,300.